Details

analyze1.4s (8.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample406.0ms (2.5%)

Algorithm

1×

intervals

Results

159.0ms	131×	body	1024	valid
70.0ms	105×	body	1024	nan
27.0ms	56×	body	512	valid
21.0ms	14×	body	2048	valid
19.0ms	46×	body	512	nan
10.0ms	29×	body	256	valid
9.0ms	31×	body	256	nan
4.0ms	26×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

61.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Status

Error

Program

▶

61.6b

(*.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.2b	(*.f64 (PI.f64) f)
✓	1.7b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
✓	7.1b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series51.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

36.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
2.0ms	(*.f64 (PI.f64) f)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 159

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
5.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
5.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
3.0ms	(*.f64 (PI.f64) f)

simplify333.0ms (2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
588×	`times-frac_binary64`
366×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
196×	`exp-prod_binary64`

Counts

207 → 258

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	8603
1	652	7401
2	1996	6651
3	4169	6609
4	4840	6609

prune367.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	345	4	349
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	346	4	350

Error

2.3b

Counts

350 → 4

Alt Table

Status	Error	Program
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 f) (cbrt.f64 f))) (cbrt.f64 f)))))) (/.f64 -4 (PI.f64)))
▶	2.6b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	2.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16052 to 10398 computations (35.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.2b	(pow.f64 (*.f64 f (PI.f64)) 3)
✓	0.4b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(pow.f64 (PI.f64) 5)

series51.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

35.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
9.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
7.0ms	(/.f64 4 (*.f64 f (PI.f64)))
0.0ms	(pow.f64 (PI.f64) 5)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
3.0ms	(/.f64 4 (*.f64 f (PI.f64)))
2.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
1.0ms	(pow.f64 (PI.f64) 5)

simplify201.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

344×	`times-frac_binary64`
328×	`associate-/l*_binary64`
315×	`fma-neg_binary64`
303×	`fma-def_binary64`
220×	`unswap-sqr_binary64`

Counts

125 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	257	3602
1	614	3215
2	2100	3188
3	4931	3183
4	5033	3183

prune330.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Error

2.0b

Counts

176 → 9

Alt Table

Status	Error	Program
▶	2.6b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	3.1b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 f) (cbrt.f64 f))) (cbrt.f64 f)))))) (/.f64 -4 (PI.f64)))
	2.9b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (*.f64 (/.f64 -4 (PI.f64)) (/.f64 -4 (PI.f64))) (/.f64 -4 (PI.f64)))))
	2.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.8b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	2.9b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	3.5b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 7547 to 4867 computations (35.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))
✓	0.3b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	1.0b	(sqrt.f64 (PI.f64))
	1.0b	(pow.f64 (PI.f64) 5)

series108.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

73.0ms

(*.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))

35.0ms

(*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))

0.0ms

(sqrt.f64 (PI.f64))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
44×	`associate-r_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`

Counts

3 → 121

Calls

3 calls:

11.0ms

(*.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))

9.0ms

(*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))

1.0ms

(sqrt.f64 (PI.f64))

simplify254.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

783×	`times-frac_binary64`
622×	`fma-def_binary64`
455×	`cancel-sign-sub-inv_binary64`
394×	`fma-neg_binary64`
277×	`associate-l_binary64`

Counts

145 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	309	8618
1	835	7379
2	2852	7306
3	4692	7304
4	5370	7304

prune387.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	243	3	246
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	248	7	255

Error

1.9b

Counts

255 → 7

Alt Table

Status	Error	Program
	2.8b	(.f64 (/.f64 (/.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (sqrt.f64 (PI.f64)))))
	2.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 f) (cbrt.f64 f))) (cbrt.f64 f)))))) (/.f64 -4 (PI.f64)))
	2.9b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
✓	2.6b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
▶	2.6b	(.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))) (/.f64 -4 (sqrt.f64 (cbrt.f64 (PI.f64)))))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 11947 to 7440 computations (37.7% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))
	1.0b	(sqrt.f64 (PI.f64))
✓	1.0b	(cbrt.f64 (PI.f64))
	1.0b	(pow.f64 (PI.f64) 5)

series0.0ms (0%)

Counts

2 → 0

Calls

2 calls:

0.0ms	(cbrt.f64 (PI.f64))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
11×	`pow-flip_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))
1.0ms	(cbrt.f64 (PI.f64))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

790×	`unswap-sqr_binary64`
764×	`fma-def_binary64`
678×	`times-frac_binary64`
498×	`fma-neg_binary64`
260×	`associate-/l*_binary64`

Counts

60 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	69	626
1	87	588
2	112	588
3	156	588
4	204	588
5	261	588
6	439	588
7	892	588
8	2468	588
9	4269	588
10	5097	588

prune236.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	144	7	151

Error

1.9b

Counts

151 → 7

Alt Table

Status	Error	Program
	2.8b	(.f64 (/.f64 (/.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (sqrt.f64 (PI.f64)))))
	2.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 f) (cbrt.f64 f))) (cbrt.f64 f)))))) (/.f64 -4 (PI.f64)))
	2.9b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
✓	2.6b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	2.6b	(.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))) (/.f64 -4 (sqrt.f64 (cbrt.f64 (PI.f64)))))
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 7647 to 4227 computations (44.7% saved)

regimes2.6s (16.1%)

Accuracy

Total 0.6b remaining (27.8%)

Threshold costs 0.6b (27.8%)

Counts

325 → 1

Compiler

Compiled 77562 to 55640 computations (28.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	61
1	32	61
2	31	61

end1.0ms (0%)

Compiler: Compiled 38 to 27 computations (28.9% saved)

sample9.3s (56.8%)

Algorithm

1×

intervals

Results

3.1s	3838×	body	1024	valid
2.3s	3820×	body	1024	nan
916.0ms	1982×	body	512	valid
866.0ms	1939×	body	512	nan
626.0ms	504×	body	2048	valid
384.0ms	1029×	body	256	valid
269.0ms	954×	body	256	nan
104.0ms	647×	body	128	valid
2.0ms	2×	body	2048	nan
0.0ms	2×	body	128	overflowed
0.0ms	1×	body	128	nan

Compiler

Compiled 360 to 251 computations (30.3% saved)

Details

analyze1.4s (8.3%)

sample406.0ms (2.5%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series51.0ms (0.3%)

rewrite39.0ms (0.2%)

simplify333.0ms (2%)

prune367.0ms (2.3%)

localize18.0ms (0.1%)

series51.0ms (0.3%)

rewrite18.0ms (0.1%)

simplify201.0ms (1.2%)

prune330.0ms (2%)

localize23.0ms (0.1%)

series108.0ms (0.7%)

rewrite39.0ms (0.2%)

simplify254.0ms (1.6%)

prune387.0ms (2.4%)

localize32.0ms (0.2%)

series0.0ms (0%)

rewrite10.0ms (0.1%)

simplify81.0ms (0.5%)

prune236.0ms (1.4%)

regimes2.6s (16.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample9.3s (56.8%)

Profiling